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Dr. Math FAQ:
probability in the
Browse High School Probability
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Selected answers to common questions:
Odds vs. probability.
- The N Targets Problem [11/15/2001]
Given n targets with equal probability of being hit by a cannon, that is,
1/n. Let X be the number of firings required to hit all the targets. What
is the expectation E(X) of X?
- Odds and Probability (A Heated Argument) [01/24/2001]
My friend and I are having a raffle. It has 40 prizes in it...
- Odds of Identical Numbers [7/1/1996]
How do you figure the odds of rolling the identical number on 6 dice in
- Odds of Left-Handedness in a Group [9/2/1996]
Assuming that 10 percent of the population is left-handed, what are the
chances of having 7 lefties in a class of 23 children?
- Odds of Winning in Dice Game of Craps [02/20/2007]
How would I calculate the odds of winning in the dice game Craps?
- Odds of Winning the PowerBall Lottery [08/29/2001]
Was the article that stated that the odds of winning the 300-million-
dollar powerball were just one in 80,089,128 correct?
- Online Lottery [02/01/2002]
What is the chance of matching the numbers? How is it calculated?
- On Spins and Surprises [10/15/2011]
Nine consecutive spins of a roulette wheel surprise a gambler unfamiliar with how to
determine the likelihood of independent events. Doctor Vogler obliges with the
requested combinations and probabilities, but only after questioning our arbitrary
preference for some events over others that may have the same -- or even longer --
- Ordering Probabilities [08/13/1997]
The proportion of people who order coffee with their dinner is .9. A
simple random sample of 144 patrons of a restaurant is taken...
- Paradox Involving Swapping Dollars [08/01/2005]
A discussion of a seeming paradox involving two people comparing
amounts of money in their wallets with the greater amount being given
to the holder of the lesser amount. At first glance it seems that
the game favors both participants, but a closer look reveals that is
not really the case.
- Past Events and Probability [04/05/2000]
Do the results of past events affect future outcomes in probability? If
they don't, why is it more likely that you will get 8 heads in 10 coin
tosses than 10 heads in those 10 tosses?
- Patterns in Pascal's Triangle [07/21/1997]
I am working on a project about Pascal's triangle trying to find as many
patterns as I can and prove them by induction.
- Paychecks and Envelopes [10/07/1997]
Five paychecks and envelopes are addressed to five different people...
- Penny-moving Game [06/24/1999]
If a penny is placed on the 3 on a number line and moved left or right
based on the flip of a coin, what is the probability of it landing on 0
BEFORE it lands on 7?
- Penny Toss [12/17/1997]
Three people each toss a penny at the same time. What is the probability
that two people get the same side of the penny and the other person gets
the opposite side?
- Percentage of Numbers Divisible by 6, 8 [03/18/2003]
What percentage of numbers is divisible by 6? by 8?
- Phone Number Combinations [05/07/2000]
Linda knows the first 3 digits of Jack's phone number, but she doesn't
know the other 4...
- Pi and Probability [12/21/1997]
I'm doing a report for my math class on the relation between pi and
- Picking Colored Balls [05/05/1997]
A bag contains an assortment of red and blue balls. Given the
probabilities of picking certain combinations of balls, determine how
many red and blue balls are in the bag.
- Picking the Same Ball [07/07/1997]
One ball is selected at random each day from a jar filled with balls.
What are the odds you will randomly select the same ball two days in a
- Playing the Lottery One Time or Weekly [06/09/2008]
Are the odds of winning higher if you purchase 10 tickets for one
lottery-style random number draw, or 1 ticket for each of 10 separate
- Point in a Circle [04/29/1997]
Given a circle with two 6-inch chords running across the top and the
bottom... find the probability that a point chosen at random is in the
region between the chords.
- Poisson and Binomial Distributions [02/22/1999]
Some assumptions made in Poisson and Binary Distributions.
- Poisson and Binomial Questions [06/13/1998]
Can you explain why the waiting time in a Poisson process is exponential?
Also, find the expected value of a binomial distribution?
- Poisson Distributions with Conditional Probability [07/22/1999]
Let X be Poisson(2), independent of Y which is Poisson(3); let W=X+Y. How
can I find the distribution of X conditional on W=10?
- Poker Hand Probabilities [02/11/1999]
What are the probabilities for all of the different types of poker hands?
- Poker Hand with At Least One Ace [04/07/2003]
What is the probability that a five-card poker hand contains at least
- Poker, Probability, Combinatorics [11/04/1997]
If we deal n hands consisting of 2 cards each, what is the probability
that there will be no pairs amoung the hands?
- Poker, the Lottery [11/08/1998]
What is the probability that a 5-card poker hand will contain cards of 5
different values? To play the Pennsylvania superlottery, a player selects
7 of the first 80 positive integers...
- Poker with a Pinochle Deck [6/30/1996]
What is the chance that a 5-card hand is a full house?
- Poker With a Pinochle Deck [7/1/1996]
If we are playing poker with a pinochle deck, what is the probability
that we can be dealt a full house?
- Popsicle Probability [02/27/2003]
There are 9 popsicles: 3 orange, 3 cherry, 3 grape. There are 4
children. What is the probability that all 4 children will get the
flavor of their choice?
- Post-Operative Complications [04/25/2002]
The rate of post-operative complication in a complex procedure is 12%.
For 40 procedures, what are the chances that the number of patients
who suffer post-operative complications will be more than ten? Less
- Powerball Odds When Buying More Tickets [12/31/2001]
If the odds are 80,000,000 to 1 of buying a winning ticket, do they go to
40,000,000 to 1 if you buy 2 tickets?
- Predicting Divisional Winners [07/29/1999]
A sportswriter "predicts" the winners of four divisions by choosing a
team completely at random in each division. What is the probability that
he will predict at least one winner correctly? What if he eliminates one
also-ran? What if he draws four names out of a hat?
- Predicting NCAA Tournament Winners [03/27/2000]
What are the odds of one person predicting the winners of all 63 games in
the NCAA Basketball Tournament?
- Predict the Population of Puffins [09/28/2002]
Scientists were studying the population of puffins in Alaska. They
spotted and tagged 52 puffins in December. Two months later, they
spotted 50 puffins. Of those 50 puffins, 3/10 of them had been tagged
in December. Predict the population of puffins in Alaska.
- Probabilities and Expected Value in Seating Arrangements [05/12/1998]
Three couples are seated at random around a round table. Let M denote the
number of husbands seated next to their wives ...
- Probabilities in a Dice Game Using Markov Analysis [03/22/2004]
Anne, Bob, and Carmel are going to take turns rolling a fair die, in
the order Anne, Bob, Carmel, Anne, Bob Carmel, etc. The first person
to roll a 6 will win $100.
a) Find the probability that Anne will win $100 if the first four
numbers rolled are 3, 2, 5, 5.
b) Find the probability that Anne will win $100 if a draw is to be
declared with nobody winning $100 in the event of a 6 not being
rolled within the first 8 rolls in total.
c) Suppose that a draw is to be declared if ever two 1's are rolled
in a row (by two different players). Also suppose that the game is
in fact over and did not end in a draw. Find the probability that
Anne is the player who won $100.
- Probabilities when Rolling 10 Dice [07/29/1999]
What are the odds of a player rolling the same numbers in the same order
as the house on 10 dice? ...of rolling the same numbers without regard to
the order in which they were rolled?